Cleveland Wright, 55, falls into thought outside his parents’ home on Aug. 17, 2013, in Washington. (Jahi Chikwendiu/Washington Post)

Prosecutors have agreed that a court should throw out the conviction of a District man who spent 28 years in prison for murder, acknowledging that flaws in their case were revealed by DNA testing that exonerated his co-defendant.

U.S. Attorney Ronald C. Machen Jr. cited discredited scientific evidence in agreeing to dismiss charges against Cleveland Wright, 55.

It is as much a prosecutor’s “duty to refrain from improper methods calculated to produce a wrongful conviction as it is to use every legitimate means to bring about a just one,” Machen wrote in court papers, quoting an oft-cited 1935 U.S. Supreme Court opinion. In the papers, signed Wednesday and received by Wright’s attorneys Friday, Machen stopped short of joining Wright’s bid for a declaration of innocence, but he said he would not try Wright again.

Wright was convicted of murdering a District floral shop worker in an early morning robbery in July 1978. He was released from prison and placed on lifetime parole in 2007.

Thirty-five years ago, Wright, then 20, and Santae Tribble, then 17, were childhood friends who were accused of teaming up to rob and kill two men using the same gun, two weeks apart, in the same Southeast Washington neighborhood.

Both defendants were charged in both killings. But Tribble was acquitted in the slaying of the flower shop worker, and Wright was acquitted in the slaying of a cabdriver.

DNA testing in 2012 indicated that prosecutors and the FBI Laboratory were incorrect in linking Tribble to a hair found in a stocking near the cabbie’s killing. A witness said the killer had worn a stocking mask, but DNA testing found that hairs in the stocking came from neither Wright nor Tribble.

In December 2012, D.C. Superior Court Judge Laura A. Cordero found that “by clear and convincing evidence,” Tribble was not guilty and that he had nothing to do with the crime of which he was convicted.

In August, Wright asked Cordero to review his conviction in the killing of the flower shop worker. “If neither of them was the masked murderer of [the first victim], then neither of them was the murderer of [the second], as the same gun was used to kill both men under similar circumstances,” wrote Sandra K. Levick, chief of special litigation for the D.C. Public Defender Service, which handled each man’s post-conviction petitions.

In its reply, Machen’s office agreed that the prosecutions’ reliance on now-discredited hair evidence should void Wright’s conviction and that the government is not in a position to develop new evidence 35 years after the slaying. Prosecutors also noted that Cordero had declared Wright’s co-defendant innocent.

“The interest of the United States ‘in a criminal prosecution is not that it shall win a case, but that justice shall be done,’ ” Machen wrote, again citing the high court’s 1935 opinion in Berger v. United States.

Machen said the government took no position on Wright’s petition for a certificate of innocence, which would help him obtain financial compensation, the same stance he took in Tribble’s case.

Levick said that Wright wept upon hearing the news Friday and that he would continue to ask the court for full exoneration.

“For 35 years Cleveland Wright has protested his innocence. Today we learned that the United States is vindicating his quest for justice,” Levick said in a written statement. “On Mr. Wright’s behalf, [the Public Defender Service] looks forward to what it hopes will be quick action by the court on our pending motion.”

The flower shop worker, William Horn, 52, was killed as he walked from his car to his apartment building about 2:30 a.m. July 13, 1978. The cabdriver, John McCormick, 63, was slain on his front porch 13 days later, after he parked his cab about 3:10 a.m. Both men were shot with .32-caliber bullets that police said were fired from the same weapon blocks from Tribble’s mother’s home.

Tribble’s case was featured in a series of reports in The Washington Post about flaws in FBI hair examinations that had led to wrongful convictions in the District and elsewhere.